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Scale Rules

Calculating Rules

In addition to length measurements, scale rules could be marked with aids for calculation. Perhaps the most notable rule of this type was Gunter's scale, which was similar to a sector or a slide rule. Gunter's scales are named after Edmund Gunter, a 17th-century English mathematical practitioner who figured out how to put a table of logarithms on a rule so that logarithmic calculations could be made with the aid of dividers. These instruments were especially handy for mathematicians and navigators.

The mathematics collections contain several other objects, ranging from the 18th to the 20th centuries, that were used to simplify computations for tasks including designing sundials, keeping track of calendar dates, and plotting data for aeronautical engineering. A few of these rules were designed specifically for positioning artillery.

The scales on this three-foot wooden rule are drawn in red and black ink on paper attached to both sides of the instrument. The left end of one side is marked: A DiALLiNg SCALE [sic]. A brass hanger is screwed into the left end. This side has an hour line, a line of latitude, a line of chords, a scale of inches divided to 1/8" and numbered by ones from 1 to 12, another line of chords, another line of latitude, and another hour line. The last three scales are approximately 3/4 the length of the first three scales. For example, the first hour line is 18" long and the second is almost 13" long.

The middle of this side has two diagrams for calculating the gnomon rods of sundials. Next are two more sets of three scales (hour line, line of latitude, and line of chords). These scales are shorter than the first two sets of scales, with the hour line for the third set measuring 6-3/8" and the fourth hour line measuring 7-3/4". Drawings of a sun and a sundial are at the right end of this side. The side is covered with brass studs for affixing pins while making up gnomons.

The other side has diagrams for a line of inclination; a line of chords; an hour line; lines of chords and latitudes; lines of longitude, chords, latitude, and rhumbs; and an hour line. Two drawings of sundial platforms are at the right end. An oak and pine case is fastened with a metal hook. Presumably a craftsman used this rule to make sundials. The Smithsonian acquired this object in 1961.

This brass measuring instrument resembles a sector, with a rounded apex and two rectangular legs. The front of the object is marked: MACHINE WHEELS. It bears a proportional scale with numbers 6, 8, 10, 16, and 20. One leg contains a proportional scale labeled "Pitch Line" (numbered 6, 8, 12, 16, 20) and a scale labeled "Depth of Tooth" that is uniformly divided into single units and numbered by tens from 20 to 160. The other leg is labeled "Gauge Point" and bears a scale uniformly divided into single units and numbered by tens from 20 to 160. Both scales are engraved with a small arrow at the 80 point. "Gauge Point" is separated from the scale by an ornate engraved arrow, so those words may refer to the proportional scale on the rounded part of the instrument. The legs bear a maker's mark: W. WRIGHT, (/) GLOSSOP. There are three posts, or mill feet, two on the legs and one at the center, on each side of the instrument, so that it stands about 3/4" away from the surface on which it rests.

The back of the object is marked: MILL GEER WHEELS. It bears a proportional scale with numbers and letters: 4, U, 12, 16, 20. ("Geer" and "gear" were both acceptable spellings in the 18th and 19th centuries.) Each leg contains a scale that is uniformly divided into single units and numbered by tens from 10 to 80. Small arrows are engraved on both legs at the 47 and 80 points. Another larger, ornate arrow on the left leg separates the words "Gauge Point" from the uniformly divided scale. The posts on the legs on this side are corroded. The instrument is stored in a mahogany case painted blue on the inside.

W. Wright manufactured instruments in the parish of Glossop in northwest Derbyshire, England, in the 18th century. Between ten and twenty cotton mills opened in Glossop in the 1790s. Wright apparently also worked at times in Manchester, 30 miles to the west. At least three other examples of this instrument were auctioned between 1996 and 2009, some marked "Glossop" and some marked "Manchester." The Smithsonian acquired this object in 1966.

This yew wood and brass rule finds the number of weeks between two dates that were up to two years apart. The months of the year are listed along the right edge, from January to December, twice. The month names are adjacent to a continuous calendar for the 24 months, with seven days per row. A brass slide to the left of the calendar is numbered from 1 to 104 (for two years of weeks). A ring at the top for hanging the rule is marked: TIME TABLE. Dock companies used the rule to compute storage charges for goods shipped to or from British ports.

The right edge is marked: DRING & FAGE MAKERS TOOLEY ST LONDON. The English firm established by John Dring and William Fage operated at various locations on Tooley Street from 1792 to 1882. For another timetable, or rent, rule by this maker, see inventory number 1954–305 at the Science Museum in South Kensington, London, http://www.sciencemuseum.org.uk/objects/mathematics/1954-305.aspx. The Science Museum owns several dozen other objects by this maker; see http://collectionsonline.nmsi.ac.uk/detail.php?type=related&kv=2628&t=people.

The back of the rule is stenciled: HWE. The Smithsonian acquired this object in 1962. No further information on the original owner is available.

This boxwood rule has six cylindrical segments with brass ends that can be screwed together to form a total length of 60 inches. One scale on the object measures inches, divided to tenths of an inch. It was used to determine the length of the diagonal of a barrel. The second scale is proportionally divided and numbered from 1 to 400. The user compared the diagonal length in inches to this scale to determine the volume of the barrel in imperial gallons, a unit of measure adopted by the United Kingdom in 1824.

The fifth segment is marked: J. LONG MAKER 43 EASTCHEAP LONDON. The firm established by Joseph Long in 1821 continued to make hydrometers and other instruments after Long's death around 1846. From 1885 to 1936, the firm was located at 43 Eastcheap Street in London.

A leather pouch has pockets for each of the segments. The flap of the pouch is marked: W.

This instrument is in the shape of a hollow octagonal prism. A pair of dividers (measuring 10.6 x 1.3 x 1.2 cm) screws into one end. One leg of the dividers may be removed and placed in a hole at the other end of the scale. A slide then moves the leg back and forth for use as a scriber.

A scale appears on each face of the instrument: inches (divided to 1/10" and numbered from 1 to 6); chords; sines; tangents; equal parts of 30, 25, and 20 to the inch; and "calibre." Many of these scales appeared on sectors; like those instruments, this object would have been used for surveying, architectural drawing, and artillery positioning.

The face with the calibre scale is marked: G. Adams LONDON. In 1734, George Adams Sr. (1709–1772) established a workshop on Fleet Street. From 1756 the firm fulfilled hundreds of commissions as instrument maker to His Majesty's Office of Ordnance. George Adams Jr. (1750–1795) took over the business after his father's death, with help from his mother, Ann, for the first couple of years. Although he retained the ordnance commissions, these became less profitable over time and the firm was in debt when he died. George Jr.'s wife, Hannah, sold the remaining stock and tools in 1796. Father and son both used the signature "G. Adams," so this instrument cannot be dated precisely.